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Service Oriented Architectures enable markets of functionally equivalent service providers delivering services at different Quality of Service (QoS) and cost levels. Under these circumstances, there is a need for mechanisms to optimally select service providers at run-time to support a business process execution so that a utility function for the business process is maximized subject to QoS and cost constraints. This is an NP-hard problem. This paper investigates this problem when the utility function is expressed in terms of multiple QoS metrics. An efficient optimal algorithm is presented, which eliminates the need to exhaustively search the state space. This algorithm can be used for small to medium size problems. A very efficient heuristic solution is also presented and scientifically evaluated against the optimal solution on a large set of randomly generated business processes.